Worst 'I've been looking at dodgy nudey emails while at work' thread!
They won't be able to see/read your emails unless they were to be stood behind you or failed into your machine via a VNC connection.
As said they'll know youve been on a web mail but that's it.
They can watch your screen remotely, log everything you do, etc. So yes, theoretically they can read your emails. However I fail to see why they would want to. Plus they would be limited to what they could do with the information anyway.
Certainly isnt illegal, if theres an IT policy and a HR policy to back it up. It would be illegal for them to access your email account separately, but not for them to monitor an employees web and email usage. HTTPS protects you to a certain extent, but its not a cloak of invisibility.